Noncovalent interactions of free-base phthalocyanine (H2Pc) with closed-cap armchair (5,5) and zigzag (10,0) single-walled carbon nanotubes (ANT and ZNT, respectively), as well as, for comparison, with C60 and C80(Ih) fullerenes, whose hemispheres were used to close the ends of nanotube models, were studied theoretically by using one pure dispersion-corrected GGA functional (PBE with a long-range dispersion correction by Grimme, or PBE+D) and two hybrid meta exchange-correlation functionals (M05-2X and M06-2X). Strong complexation was observed in all four systems studied. The general trend found is that the interaction strength increases with the size (number of C atoms) of carbon nanocluster, that is, in the order of ZNT > ANT > C80 > C60. Depending on the DFT functional employed, the interaction strength decreased in the order of PBE+D > M06-2X > M05-2X. A common feature for the geometry of all four complexes considered, reproduced in all the calculations, is that H2Pc macrocycle undergoes strong distortion, which allows for increasing its contact surface with the nanotube sidewall or spherical fullerene, and therefore makes π-π interactions more efficient.